 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/digital-systems-linear-algebra-introduction-to-formal-proof/4/c/iii/solution

A triangular matrix has determinant equal to the product of its diagonal entries, so

det L = 1

and

det U = 3 \cdot 4 \cdot (- 11) = - 132

- 1

. Using multiplicativity of the determinant in

P A = LU

yields

(- 1) det A = - 132

. Hence $det A = 132$ .

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